The first choice is to start with our map and then save it to your own ArcGIS Online account (either a free, public account that has restrictions or an existing organizational account). Under this scenario, you are saving a copy of our map and can therefore make changes like adding or removing layers, changing the appearance and extent and sharing. It is a copy so you are not changing our original map (and cannot even if you tried).
The second choice is to start with a new Map and then add the layers.
Sign In to ArcGIS Online using your own account.
Choose Save As to save a copy of the map to your own account. Note that your map is now disconnected from our original map. You are not changing our map and any changes we make to our map will not be reflected on your map.
Use the ArcGIS Online Map Viewer to make any changes or additions to the map.
Click on Map to open a new, blank map the in the ArcGIS Online Map Viewer.
To add the elevation layers to the map, click on Add and choose Search for Layers.
The elevation layers available are listed. Click Add next to any or all of the layers that you would like to add to your map. When finished, click Done Adding Layers at the bottom of the left panel.
Continue to create your map as normal in ArcGIS Online. Be sure to save it when you are finished.